Question

If a spherical ball rolls on a table without slipping the friction of its total energy associated with rotational energy is:

• A. 3/5
• B. 2/7
• C. 2/5
• D. 3/7

Answer 1

Answer: (B)

Rotational energy of sphere
$E_R=\frac{1}{2}I{\omega }^2$
For sphere, moment of inertia
$I=\frac{2}{5}m{R}^2$
$\therefore E_R=\frac{1}{2}\left(\frac{2}{5}m{R}^2\right){\left(\frac{v}{R}\right)}^2$
$=\frac{1}{5}m{v}^2$
Translational kinetic energy $E_r=\frac{1}{2}m{v}^2$
$\therefore$ Total energy $=\frac{1}{5}m{v}^2+\frac{1}{2}m{v}^2$
$=\frac{7}{10}m{v}^2$
$\therefore$ Required fraction
$=\frac{\frac{1}{5}m{v}^2}{\frac{7}{10}m{v}^2}$
$=\frac{2}{7}$